Partial Matching of Nonrigid Shapes by Learning Piecewise Smooth Functions

Abstract

Learning functions defined on non-flat domains, such as outer surfaces of non-rigid shapes, is a central task in computer vision and geometry processing. Recent studies have explored the use of neural fields to represent functions like light reflections in volumetric domains and textures on curved surfaces by operating in the embedding space. Here, we choose a different line of thought and introduce a novel formulation of partial shape matching by learning a piecewise smooth function on a surface. Our method begins with pairing sparse landmarks defined on a full shape and its part, using feature similarity. Next, a neural representation is optimized to fit these landmarks, efficiently interpolating between the matched features that act as anchors. This process results in a function that accurately captures the partiality. Unlike previous methods, the proposed neural model of functions is intrinsically defined on the given curved surface, rather than the classical embedding Euclidean space. This representation is shown to be particularly well-suited for representing piecewise smooth functions. We further extend the proposed framework to the more challenging part-to-part setting, where both shapes exhibit missing parts. Comprehensive experiments highlight that the proposed method effectively addresses partiality in shape matching and significantly outperforms leading state-of-the-art methods in challenging benchmarks. Code is available at https://github.com/davidgip74/ Learning-Partiality-with-Implicit-Intrinsic-Functions